Equilibrium free energies from nonequilibrium simulations: Improving convergence by reducing dissipation

The estimation of equilibrium free energy differences is an important problem in computational thermodynamics, with applications to studies of ligand binding, phase coexistence and phase equilibrium, solvation of small molecules, and computational drug design, among others. Recent advances in nonequilibrium statistical mechanics, in particular the discovery of exact nonequilibrium work fluctuation relations, have made it possible to estimate equilibrium free energy differences from simulations of nonequilibrium processes in which a system of interest is driven irreversibly between two equilibrium states. Estimates of the free energy difference obtained from processes in which the system is driven far from equilibrium often suffer from poor convergence as a consequence of the dissipation that typically accompanies such processes. This thesis is concerned with this problem of poor convergence, and studies methods to improve the efficiency of such estimators. A central theoretical result that guides the development of these methods is a quantitative connection between dissipation and the extent to which the system ``lags'' behind the actual equilibrium state, at any point in time of the nonequilibrium process. The first strategy involves generating ``escorted" trajectories in the nonequilibrium simulation by introducing artificial terms that directly couple the evolution of the system to changes in the external parameter. Estimators for the free energy difference in terms of these artificial trajectories are developed and it is shown that whenever the artificial dynamics manage to reduce the lag, the convergence of the free energy estimate is improved. We demonstrate the effectiveness of this method on a few model systems. In particular, we demonstrate how this method can be used to obtain efficient estimates of solvation free energies of model hard sphere solutes in water and other solvents. In the second strategy,``protocol postprocessing", the trajectories normally generated in the course of a nonequilibrium simulation are used to construct estimators of the free energy difference that converge faster than the usual estimators. Again, the connection between dissipation and lag guides the development of this method. The effectiveness of this strategy is also demonstrated on a few model systems

Topological localization in out-of-equilibrium dissipative systems

In this paper we report that notions of topological protection can be applied to stationary configurations that are driven far from equilibrium by active, dissipative processes. We show this for physically two disparate cases : stochastic networks governed by microscopic single particle dynamics as well as collections of driven, interacting particles described by coarse-grained hydrodynamic theory. In both cases, the presence of dissipative couplings to the environment that break time reversal symmetry are crucial to ensuring topologically protection. These examples constitute proof of principle that notions of topological protection, established in the context of electronic and mechanical systems, do indeed extend generically to processes that operate out of equilibrium. Such topologically robust boundary modes have implications for both biological and synthetic systems.Comment: 11 pages, 4 figures (SI: 8 pages 3 figures

How dissipation constrains fluctuations in nonequilibrium liquids: Diffusion, structure and biased interactions

The dynamics and structure of nonequilibrium liquids, driven by non-conservative forces which can be either external or internal, generically hold the signature of the net dissipation of energy in the thermostat. Yet, disentangling precisely how dissipation changes collective effects remains challenging in many-body systems due to the complex interplay between driving and particle interactions. First, we combine explicit coarse-graining and stochastic calculus to obtain simple relations between diffusion, density correlations and dissipation in nonequilibrium liquids. Based on these results, we consider large-deviation biased ensembles where trajectories mimic the effect of an external drive. The choice of the biasing function is informed by the connection between dissipation and structure derived in the first part. Using analytical and computational techniques, we show that biasing trajectories effectively renormalizes interactions in a controlled manner, thus providing intuition on how driving forces can lead to spatial organization and collective dynamics. Altogether, our results show how tuning dissipation provides a route to alter the structure and dynamics of liquids and soft materials.Comment: 21 pages, 7 figure